Our Arabic decimal system of numbering has served us well for nearly 2,000 years. However, the advantages of digital instruments using the binary numbering system indicate that the Arabic system should be permitted to pass into honored retirement. Typical of the instruments which can advantageously use the binary system is the 8 bit digital voltmeter. It may be compared with an 8-bit decimal unit. The decimal unit must change scales by a factor of 10. The binary unit may change scales by a factor of 2. Consequently:
Decimal Binary ______________________________________ Maximum Count 99 255 Consequent Best 1% 0.4% Resolution Minimum Count 10 128 Consequent Worst 10% 0.8% Resolution ______________________________________ A voltmeter having a resolution of 10% would hardly be useful for any purpose. Consequently two-digit decimal voltmeters are not made. But a voltmeter having a worst case resolution of 0.8% can be very useful. Consequently many 8-bit A/D converters are in use today. They are less costly than their decimal counterparts. Their performance is vastly superior. In this case it is clear that the decimal system should be dropped in favor of the binary system. The present invention drops the decimal system and introduces new tecniques which exploit fully the advantages of the binary system.
The chief object to use of the binary system is the proliferation of digits which must be quoted. In the voltmeter case cited above only two words must be uttered to express the voltage in decimal units. Eight words are necessary if the binary system is used. This shortcoming of the binary system is overcome in the present invention by adopting the base-16 numbering system. Binary digits may be grouped in groups of four to form base-16 digits. A number expressed in base-16 will generally consist of fewer words than the same number expressed in decimal units.